Method for performing a voltage stability security assessment for a power transmission system

ABSTRACT

A method for performing a voltage stability security assessment for a region of an electric power transmission system having a plurality of buses and a plurality of sources of reactive reserves coupled thereto. The plurality of buses are grouped into a plurality of voltage control areas such that each of the buses within each voltage control area has a substantially similar reactive margin and voltage at the minimum of the corresponding reactive power versus voltage relationship. A corresponding reactive reserve basin is determined for each of at least one of the voltage control areas. Each reactive reserve basin comprises at least one of the sources of reactive reserves selected in dependence upon a measure of the reactive reserves depleted at a predetermined operating point of the electric power transmission system. A single contingency analysis is performed by computing a corresponding quantity for each reactive reserve basin in response to each of a plurality of single contingencies. The corresponding quantity is representative of a reduction in the reactive reserves within the reactive reserve basin. A multiple contingency analysis is performed for each reactive reserve basin using the single contingencies whose corresponding quantity exceeds a predetermined threshold.

This is a continuation of application Ser. No. 08/236,526 filed on Apr.29, 1994, now abandoned.

TECHNICAL FIELD

This invention relates generally to planning of electrical powertransmission systems, and more particularly, to a method for performinga voltage stability assessment for power transmission systems.

BACKGROUND ART

There are a number of potential voltage instability problems which canarise within an electrical power system. Some of these instabilityproblems occur in distribution systems used for distributing electricalpower to utility customers. Many of the sources of these distributionsystem voltage stability problems have existed for years, and theircauses and solutions are well known in the art.

Other problems occur in transmission systems, which are used fortransporting bulk power from generation stations to load centers. Thesestability problems result from such causes as facility outages, clearingof short circuit faults, and increases in load power or inter-area powertransfer in a transmission network. Many of these transmission systemvoltage instability problems have been encountered only in recent years.These instability problems have occurred as a result of recent trendstoward: locating generation stations distantly from load centers whichlimits the effectiveness of their voltage controls, requiring utilitiesallow power shipment across their transmission system by independentpower producers or other utilities, and deterring construction of neededtransmission networks, to name a few.

A slow-spreading, uncontrollable decline in voltage, known as voltagecollapse, is a specific type of transmission system voltage instability.Voltage collapse results when generators reach their field currentlimits which causes a disabling of their excitation voltage controlsystems. Voltage collapse has recently caused major blackouts in anumber of different countries around the world.

In order to reduce the possibility of voltage collapse in a powersystem, and more generally, improve the stability of the power system,system planning is performed by many utility companies. First, amathematical model representative of the basic elements of the powersystem, and their interconnection, is constructed. These basic elementsinclude generating stations, transformers, transmission lines, andsources of reactive reserves such as synchronous voltage condensers andcapacitor banks. Next, various computational techniques for analyzingsystem stability are performed using a suitably programmed computer.Based on this analysis, proposed enhancements are formulated in anad-hoc manner for improving voltage stability security. The mathematicalmodel can be updated based upon these proposed enhancements so that theresulting system stability security can be analyzed. Enhancements whichattain predetermined design objectives are then physically implementedin the actual power system. The process of system planning is continualin that it must be regularly performed in light of changingcircumstances.

In mathematical terms, voltage collapse occurs when equilibriumequations associated with the mathematical model of the transmissionsystem do not have unique local solutions. This results either when alocal solution does not exist or when multiple solutions exist. Thepoint at which the equilibrium equations no longer have a solution or aunique solution is often associated with some physical or controlcapability limit of the power system.

Current methods for assessing proximity to classic voltage instabilityare based on some measure of how close a load flow Jacobian is to asingularity condition, since a singular load flow Jacobian implies thatthere is not a unique solution. These proximity measures include: (i)the smallest eigenvalue approaching zero, (ii) the minimum singularvalue, (iii) various sensitivity matrices, (iv) the reactive powerflow-voltage level (Q-V) curve margin, (v) the real power flow-voltagelevel (P-V) curve margin, and (vi) eigenvalue approximation measures ofload flow Jacobian singularity.

The eigenvalue and minimum singular value methods are disadvantageous intheir lacking an indication of the actual locations and causes ofvoltage instability. Moreover, these methods have been known to producemisleading results with respect to causes of voltage instability as wellas the locations and types of enhancements necessary to improve voltagestability security. Furthermore, the computational requirements for theeigenvalue and minimum singular value methods are relatively high. Thesensitivity matrix methods have many of the same difficulties as theeigenvalue and singular value methods resulting from being linearincremental measures for a highly-nonlinear discontinuous process.

Regardless of the method employed for assessing proximity to classicvoltage instability, existing methods employed by many utility companiesassume that there is only one voltage instability problem. Further, itis assumed that one distributed reactive power loading pattern testdetects the one voltage instability problem.

It is known that a voltage control area may be defined as anelectrically isolated bus group in a power system. Reactive reserves ineach voltage control area may be distributed via secondary voltagecontrol so that no generator or station would exhaust reserves beforeall the other generators in the voltage control area. Although thissecondary voltage control is effective in preventing classic voltageinstability, previously defined voltage control areas are no longervalid whenever the originally existing transmission grid is enhanced sothat bus groups are no longer as isolated. A further disadvantage ofthis approach is that the reactive reserves for controlling each voltagecontrol area are limited to be within the voltage control area.

Methods are also known which employ a voltage zone defined as a group ofone or more tightly-coupled generator P-V buses together with the unionof the sets of load buses they mutually support. In such methods, amountof reactive power supply to maintain an acceptable voltage level iscontrolled. A disadvantage of this approach, however, is thatcharacterizing a voltage stability margin in terms of voltage does notprotect against classic voltage collapse.

Current engineering methods of locating potential voltage instabilityproblems includes simulating all single line outage contingencies, andidentifying those that do not solve as causing voltage instability.However, the lack of a solution is not a guarantee of voltageinstability; a lack of a solution can occur because: the load flowNewton-Raphson-based algorithms are not guaranteed to converge from anyparticular starting solution, but converge only when the starting pointis sufficiently close to the solution; the load flow convergence is notguaranteed even when the system is close to a solution if the solutionis close to a bifurcation; round-off error affects the load flowconvergence; and discontinuous changes due to switching of shuntelements, or outages of generators or lines can have a dramatic effecton whether the load flow algorithm will converge to a solution. Theconverged solutions for all single outages only indicates that there areno bifurcations. In order to attempt to prove that the absence of aconverged solution is caused by voltage instability, substantialmanpower and computer processing time are required. In one such method,the absence of a converged solution is determined to be due to voltagecollapse if one can add a fictitious generator with infinite reactivesupply at some bus to obtain a converged load flow solution. This methodis not foolproof, and furthermore, does not indicate the causes ofvoltage instability nor indicate where it occurs.

However, current methods are incapable of identifying all of the manydifferent voltage stability problems that can occur in a transmissionsystem. A very routine operating change or supposedly insignificantcontingency in a remote region of the system, followed by anothercontingency, can cause voltage instability. Furthermore, voltageinstability may occur in many different sub-regions of the system.Current methods lack diagnostic procedures for identifying causes ofspecific voltage stability problems, as well as systematic andintelligent enhancement procedures for preventing voltage instabilityproblems.

SUMMARY OF THE INVENTION

For the foregoing reasons, the need exists for a method of identifyingpotential locations of voltage instability problems, and determiningcorrective measures to reduce the likelihood of voltage instability.

It is thus an object of the present invention to provide an improvedmethod for determining potential voltage instability problems in anelectrical power transmission system.

Another object of the present invention is to provide a method ofidentifying single contingencies that cause voltage instability in anelectrical power transmission system. A further object is to provide amethod of identifying multiple contingencies, transfer patterns andlevels, and loading patterns and levels that cause voltage instabilityin an electrical power transmission system.

In carrying out the above objects, the present invention provides amethod of performing a contingency analysis for a region of an electricpower transmission system having a plurality of buses and a plurality ofsources of reactive reserves coupled thereto. The plurality of buses aregrouped into a plurality of voltage control areas such that each of thebuses within each voltage control area has a similar correspondingreactive power versus voltage relationship. A corresponding reactivereserve basin for each of at least one of the voltage control areas isdetermined. Each reactive reserve basin comprises at least one of thesources of reactive reserves selected in dependence upon a measure ofthe reactive reserves depleted at a predetermined operating point of thepower system. A single contingency analysis is performed by computing acorresponding quantity for each reactive reserve basin in response toeach of a plurality of single contingencies. The corresponding quantityis representative of a reduction in the reactive reserves within thereactive reserve basin. A multiple contingency analysis is performed foreach reactive reserve basin based upon the single contingencies whosecorresponding quantity exceeds a predetermined threshold.

The present invention further provides a method of performing a voltagestability assessment for a region of an electric power transmissionsystem having a plurality of buses and a plurality of sources ofreactive reserves coupled thereto. The plurality of buses are groupedinto a plurality of voltage control areas such that each of the baseswithin each voltage control area has a similar corresponding reactivepower versus voltage relationship. At least one of the voltage controlareas whose buses therewithin have a voltage at the minimum of thecorresponding reactive power versus voltage relationship which exceeds avoltage threshold is selected. A corresponding reactive reserve basin isdetermined for each of the at least one of the voltage control areas,wherein the reactive reserve basin comprises at least one of the sourcesof reactive reserves selected in dependence upon a measure of thereactive reserves depleted at a predetermined operating point of theelectric power transmission system. A single contingency analysis isperformed by computing a corresponding quantity for each reactivereserve basin in response to each of a plurality of single faultcontingencies, wherein the corresponding quantity is representative of areduction in the reactive reserves within the reactive reserve basin,and wherein the plurality of single contingencies includes at least onesingle generator outage and at least one single line outage. The singlecontingencies whose corresponding quantity exceeds a predeterminedthreshold are selected. The voltage stability for single and multiplecontingencies with a plurality of transfer and loading patterns areassessed, wherein the single and multiple contingencies are based uponthe selected single contingencies.

These and other objects, features and advantages will be readilyapparent upon consideration of the following description, appendedclaims, and accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow chart of performing a contingency analysis according tothe method of the present invention;

FIG. 2 is a flow chart of grouping buses into voltage control areasaccording to the method of the present invention;

FIG. 3 is a flow chart of determining a reactive reserve basin accordingto the method of the present invention;

FIG. 4 is a flow chart of performing a single contingency analysisaccording to the method of the present invention;

FIG. 5 is a flow chart of performing a multiple contingency analysisaccording to the method of the present invention;

FIG. 6 is a flow chart of determining voltage control areas according tothe method of the present invention;

FIG. 7 is a flow chart of performing a contingency selection accordingto the method of the present invention;

FIG. 8 is a flow chart performing a reactive reserve basin securityassessment according to the method of the present invention;

FIG. 9 is a flow chart demonstrating robustness of the reactive reservebasins according to the method of the present invention; and

FIG. 10 is a flow chart performing a stability security assessmentaccording to the method of the present invention.

BEST MODES FOR CARRYING OUT THE INVENTION

The method of the present invention overcomes the disadvantages ofprevious security assessment methods and systems by intelligentlyselecting single contingencies used in performing a multiple contingencyanalysis. More specifically, the single contingencies used in performingthe multiple contingency analysis are selected based upon the reductionin reactive reserves in a region of the electrical power transmissionsystem known as a reactive reserve basin. Moreover, the method of thepresent invention produces a hierarchical control structure wherein alack of controllability provides evidence of a potential voltageinstability problem.

In general, the method of the present invention is capable ofidentifying totally independent voltage stability problems that affectfairly isolated sections of one or more utilities. A unique voltagestability problem occurs when a Q-V curve computed at any bus in asufficiently coherent group has the same shape, minimum, and reactivereserve basin. The neighboring voltage control areas with reactivesupply devices that exhaust nearly all reactive reserves upon reachingthe minimum of the Q-V curve computed in some critical voltage controlarea is a reactive reserve basin for that critical voltage control area.A global voltage stability problem occurs when the reactive reserves ina large number of voltage control areas are exhausted. Global reactivereserve basins for different voltage stability problems do not containany of the same voltage control areas. Each global voltage stabilityproblem is prevented by a unique and non-overlapping set of reactivesupply devices belonging to its reactive reserve basin.

For each global stability problem, a large set of local stabilityproblems lie nested therewithin. In turn, each local stability problemhas a different reactive reserve basin associated therewith. However,these local reactive reserve basins overlap. As a result, thepossibility exists that a generator, switchable shunt capacitor or SVCbelongs to several local reactive reserve basins.

When the reactive reserves in a voltage control area are exhausted, allreactive reserve basins to which that voltage control area belongsexperience a significant step change toward voltage instability. Thelocal reactive reserve basin that exhausts all reactive reserves in allvoltage control areas due to contingencies or operating changes is thelocal reactive reserve basin that experiences voltage instability, aslong as the contingencies or operating changes directly impact thecritical voltage control area where the Q-V curve is computed todetermine that reactive reserve basin. The exhaustion of all reactivereserves for all voltage control areas in a local reactive reserve basinproduces voltage instability for that critical voltage control areabecause that critical voltage control area cannot obtain all thereactive supply needed to cope with the contingencies or operatingchanges. As used herein, a contingency may be any unexpected discretechange in the transmission system due to equipment loss (such as agenerator, transmission line, or transformer) or a short circuit(typically referred to as a fault contingency).

A locally most vulnerable critical voltage control area and reactivereserve basin is one that belongs to almost every local reactive reservebasin also belonging to a global reactive reserve basin. This locallymost vulnerable reactive reserve basin has relatively small reservesthat exhaust rapidly for Q-V curve stress tests computed for almostevery local critical voltage control area which has local reactivereserve basins that are subsets of a global reactive reserve basin. Suchlocally most vulnerable reactive reserve basins should be the focus ofany system enhancements.

It should be noted that local voltage stability problems are thosebrought on by contingencies or operating changes and not the globalvoltage stability problems which would most often only develop out of aspreading local voltage stability problem. Generally, all such localvoltage stability problems need be addressed, not just the locally mostvulnerable. This is so because each local stability problem, includingthe locally most vulnerable, may be brought on by differentcontingencies or operating changes that cause reduction of, or partiallycut off, the reactive reserves associated with the critical voltagecontrol area.

More specifically, the method of the present invention employs Q-V curvetests for determining a hierarchical control structure which indicatesthat voltage instability occurs when a lack of controllability isevident. Performing a multiple contingency analysis is illustrated bythe flow chart shown in FIG. 1. The multiple contingency analysis is tobe performed for a region of a power system having a plurality of busesand a plurality of sources of reactive reserves coupled thereto.

In block 100, the plurality of buses are grouped into voltage controlareas in dependence upon a corresponding reactive power versus voltagerelationship for each of the buses. More specifically, each voltagecontrol area is defined as a coherent bus group where adding a reactiveload at any bus in the group produces nearly identical Q-V curves inboth shape and magnitude. As a result, each voltage control area has aunique voltage instability caused by a local incremental reactive supplyproblem.

In block 102, determining a corresponding reactive reserve basin foreach of at least one of the voltage control areas is performed. Eachreactive reserve basin comprises at least one source of reactivereserves selected in dependence upon a quantity representative of thereactive reserves exhausted at a predetermined operating point of thepower system. The at least one source of reactive reserves containedwithin the reactive reserve basin form a set of stabilizing controls forthe corresponding voltage control area. Preferably, the predeterminedoperating point of the power system is the minimum of the Q-V curve. Itis also preferred that the total reserves in a voltage control area bedepleted by a certain percentage and/or below a certain level before thereactive sources in the voltage control area added to a reactive reservebasin.

A single contingency analysis is performed by block 104. Morespecifically, a quantity representative of the reactive reservesdepleted in response to each of a plurality of single contingencies iscomputed. These single contingencies include single line outages andsingle generator outages. Using the information computed in the singlecontingency analysis, a multiple contingency analysis is performed inblock 106. The multiple contingencies selected for analysis comprise atleast two of the single contingencies whose corresponding reactivereserve depletion quantity exceeds a predetermined threshold. Themultiple contingency analysis is performed for at least one reactivereserve basin.

In FIG. 2, a flow chart illustrates grouping the buses into voltagecontrol areas in accordance with the present invention. Voltage controlareas are defined as coherent bus groups where the Q-V curve computed atany bus in that coherent group has virtually identical voltage andreactive margin at the Q-V curve minimum. Furthermore, the shape andslope of the Q-V curve computed at any bus in the voltage control areashould be nearly identical. Based on the above definition, the voltagecontrol areas are determined using a coherent group clusteringalgorithm. An initial value of a control parameter, alpha, for theclustering algorithm is selected in block 120. The coherent groupclustering algorithm employed is based on eliminating the weakestconnections from each network bus until the sum of reactivepower-voltage Jacobian elements for eliminated branches is less than aparameter alpha times the largest diagonal element of the reactivepower-voltage Jacobian matrix. The isolated bus groups identified for aparticular alpha are the coherent bus groups for that alpha value. Thisstep of isolating bus groups in dependence upon the alpha parameter isillustrated by block 122.

For smaller values of alpha selected in block 120, the bus groups arecontinuously split until each bus group comprises a single bus. On thecontrary, if alpha is selected to be relatively large in block 120, allbuses belong to one bus group. In block 124, a level of coherency withinbus groups as well as a concomitant incoherency between bus groups isexamined based upon the Q-V curves. In particular, the Q-V curves areexamined to determine whether all buses in each bus cluster havesubstantially the same Q-V curve minimum. If the Q-V curve minima arenot substantially the same, then flow of the routine is directed back upto block 120 where a new value of alpha is selected. If the Q-V curveminima are substantially the same, then the routine is exited by returnblock 126.

Determining the reactive reserve basin for each of at least one of thevoltage control areas is illustrated by the flow chart in FIG. 3. Inblock 140, a set of test voltage control areas is selected. The selectedtest voltage control areas are those that have large shunt capacitivesupply, or an increase in reactive loss or reactive supply as Q-V curvesare computed in neighboring test voltage control areas. Line charging,shunt capacitive withdrawal, series I² X series reactive loss, increasedreactive inductive or capacitive shunts due to under load tap changers,or switchable shunt capacitors or reactors cause the increase inreactive loss or supply in a voltage control area. A Q-V curve iscomputed in each test voltage control area that has satisfied theseconditions as Q-V curves were computed in other voltage control areas.Reactive reserve basins are only determined for those test voltagecontrol areas, called critical voltage control areas, with Q-V curveshaving a large voltage and a small reactive margin at the minimum of theQ-V curve. In practice, the minimum of the Q-V curve can be obtainedusing a standard Newton-Raphson algorithm.

For each critical voltage control area, the voltage control areas whichexperience a reduction in reserves greater than a predeterminedthreshold at the Q-V curve minimum is selected in block 142. Inpractice, the predetermined threshold is measured on a relative scaleand is selected to be less than 100%. In one embodiment, the reactivereserve basin includes voltage control areas which experience greaterthan 75% reduction in reserves in computing the Q-V curve down to theQ-V curve minimum. This logic is aimed at guaranteeing that everyreactive reserve basin is robust in the sense that no contingency oroperating change that causes voltage instability on the test voltagecontrol area can exhaust all of the reactive supply and voltage controlreserve in a voltage control area outside those voltage control areascontained in the reactive reserve basin computed.

In the flow chart of FIG. 3, the reactive reserve basins are computedonly for the selected subset of voltage control areas that are predictedto be vulnerable to voltage instability by having large capacitivesupply, experiencing large shunt capacitive supply increases, orexperiencing inductive increases as Q-V curves are computed in othertest voltage control areas having Q-V curve voltage minima greater thana threshold and reactive minima smaller than another threshold.Moreover, the use of reactive reserve quantities provides anaccumulative proximity measure that makes voltage stability assessmentpractical because it is an exhaustible resource that always correlateswell with proximity to voltage instability and is easily computed for acontingency.

In such a manner, unique global voltage stability problems can beidentified that have large numbers of voltage control areas and arenearly disjoint. Most, if not all, voltage stability problems that everoccur are local. Moreover, a multiplicity of local voltage stabilityproblems are associated with each global voltage stability problem.Indeed, local voltage stability problems may be determined with a localreactive reserve basin that is substantially a subset of some globalreactive reserve basin. Identifying critical voltage control areas foreach local stability problem and their reactive reserve basinsidentifies the location of each stability problem, what reactivereserves prevent each local stability problem from occurring, and whyeach local voltage instability occurs.

Still further, the locally most vulnerable reactive reserve basin may bedetermined that lies within virtually every other local reactive reservebasin according to the Q-V curve with nearly the largest voltage maximaand nearly the smallest reactive minima. Thereafter, its reserves arerapidly exhausted for the Q-V curve computed in the critical voltagecontrol areas associated with the global and all nested local reactivereserve basins. However, despite the fact that the Q-V curve may havethe largest voltage minima and the largest reactive margin, it may notbe the most probable local voltage stability problem because there maynot be severe contingencies that directly impact its critical voltagecontrol area because it lies in a remote and low voltage part of thesystem. This leads to contingency selection for each local reactivereserve basin where in some utilities the same contingencies affect theglobal and all locals, and yet in other utilities differentcontingencies affect different locals within a global reactive reservebasin.

Performing a single contingency analysis is illustrated by the flowchart in FIG. 4. This single contingency analysis is performed for eachcritical voltage control area and its associated reactive reserve basin.In block 160, a single contingency is simulated. Specific types ofsingle contingencies include single generator outages and single lineoutages. The reactive reserves in each reactive reserve basin arecomputed for the single contingency in block 162. Conditional block 164examines whether there are more single contingencies to be simulated. Ifso, flow of the routine is directed back up to block 160 where anothersingle contingency is simulated. If no further contingencies are to besimulated, then the contingencies in each reactive reserve basin areranked from smallest to largest based upon the reactive reservesexhausted by block 166. In block 168, the single line outages whichexhaust more than a predetermined percentage of the reserves in eachvoltage control area are listed.

In block 170, the two largest reactive capacity generators in eachreactive reserve basin which exhaust more than a predeterminedpercentage of its reserve for some contingency are selected. Thesegenerators are placed on a generators list. The two lists formed inblocks 168 and 170 are used in forming multiple contingencies in asubsequent multiple contingency analysis.

Performing multiple contingency analysis is illustrated by the flowchart in FIG. 5. Using the list of single contingencies formed in block168, a list of double line outages is formed in block 180. Similarly,using the list of generators formed in block 170, a list of doublegenerator outages is formed in block 182. In block 184, a combination ofline and generator outages from the lists formed in blocks 168 and 170are used to form a combination list. The step of performing an analysisof contingencies based upon the lists produced in blocks 180, 182, and184, is illustrated by block 186.

Software for determining the voltage control areas is illustrated by theflow chart in FIG. 6. In block 200, an initialization step is performedwherein a seed bus, a number of branches, and a minimum voltage levelare selected in order to define a region of interest. Next, the Q-Vcurves are run and reactive reserve basins are determined at all busesin the region of interest in block 202. In block 204, a voting procedureis employed to select alpha where the Q-V curves computed at all busesin each bus cluster has substantially the same Q-V curve minimum andreactive reserve basin. The parameter alpha decides the size of thecoherent bus clusters which form voltage control areas. As alphadecreases, the size of the coherent bus clusters increases throughaggregation of coherent bus clusters identified for larger alpha values.This search procedure eliminates the need for a user to make a judgmenton where the differences in voltage changes at buses within coherent busgroups increases from very small values, and the voltage changedifferences between buses in different bus groups for a disturbancesuddenly increase to large values as alpha decreases.

In the search procedure for alpha, a bounded interval of potentialvalues of alpha is first selected. The procedure places a disturbance,namely a voltage change at some seed bus, and calculates the changes involtage and angle at each bus due to the disturbance. The procedurefinds bus clusters for ten equally-spaced alpha values in this boundedinterval, and then finds the smallest alpha value where the voltage andangle changes within the bus group satisfy the following equations:

    ΔV.sub.j -ΔV.sub.i ≦k.sub.1 ΔV.sub.i

    Δθ.sub.j -Δθ.sub.i ≦k.sub.2 Δθ.sub.i

where ΔV is a voltage change, Δθis an angle change, i and j are indicesrepresenting two buses within a bus group, and k₁ and k₂ are fixedparameters.

The results are confirmed as voltage control areas by running Q-V curvesat all buses in the voltage control areas to establish if alpha wasselected properly such that the minima of the Q-V curves and thereactive reserve basin obtained from the minima of the Q-V curves areidentical. If the alpha value was chosen correctly so that the Q-V curveminima and reactive reserve basins computed at every bus in the busclusters selected are identical, the user has obtained the voltagecontrol areas and proper alpha value for obtaining these voltage controlareas. If the alpha value was not correctly selected because the Q-Vcurve minima and reactive reserve basins are not identical for buses ina voltage control area, several larger values of alpha that producesmaller bus cluster groups can be examined until bus clusters which havenearly identical Q-V curve minima and reactive reserve basins are found.Hence, computing voltage control areas in this manner is based on boththe level of coherency within bus clusters and the level of incoherencyacross bus clusters.

Alternative embodiments can be formed which explicitly use thedefinition of voltage control area in order to find alpha. Morespecifically, an alternative embodiment would search for the value ofalpha that is as small as possible, i.e. which produces the largest buscluster, and yet assures that the Q-V curves computed at every bus ineach bus cluster has nearly identical Q-V curve minima and reactivereserve basins. The search for alpha would only concentrate on busclusters in some region of interest, which are buses above a certainvoltage rating and at most three circuit branches from some seed bus.

Turning now to FIG. 7, a flow chart of a contingency selection programis illustrated. As seen therein, a contingency selection and ranking forcontingencies and operating changes that bring a particular test voltagecontrol area and its reactive reserve basin closest to voltageinstability is performed. The contingency selection and rankings areperformed for each critical voltage control area and associated reactivereserve basin.

In block 210, a single line outage contingency is simulated. Thereserves in each reactive reserve basin are computed for thatcontingency in block 212. In conditional block 214, it is determinedwhether or not there are any other contingencies to be simulated. Ifthere are further contingencies to be simulated, then flow of the methodis returned back to block 210. If there are no additional contingenciesto be simulated, then flow of the routine advances to block 216.

In block 216, the contingencies are ranked in each reactive reservebasin based upon reactive reserves. In block 218, the line outages thatexhaust more than P% of the reserves in each voltage control area areselected and placed in a list. Further, the largest two reactivecapacity generators in each reactive reserve basin that exhausts P% ofits reserve for some line outage are also selected. These generators areplaced in another list. The list of generators is used to produce a setof severe single and double generator outage contingencies. The list ofline outages are used to produce a set of severe single and double lineoutage contingencies. The list of generators and line outages is used toproduce a set of combination line outage and loss of generationcontingencies.

In block 220, the severe single and multiple contingencies are simulatedand ranked based upon the reactive reserve in a reactive reserve basin.The contingency selection routine can be run several times in sequenceto obtain all of the information on why particular reactive reservebasins are vulnerable to voltage instability. The initial run wouldentail taking all single line outages in one or more areas, or in one ormore zones or areas where voltage instability is to be studied, or inthe entire system model.

In a preferred embodiment, the contingency selection routine wouldoutput a report summarizing the effects of the worst five contingenciesfor each critical reactive reserve basin. The output for each reactivereserve basin has an initial summary of the status in thepre-contingency case, including the bus names and numbers for all busesin each of the reactive reserve basin voltage control areas, thereactive supply capacity and reserves for generators, synchronouscondensers, and switchable shunt capacitors at the bus where thecomponent is located.

After the initial status of a reactive reserve basin is provided, thefive worst contingencies for that reactive reserve basin are given. Eachcontingency is described and the reactive supply reserves at allgenerators and switchable shunt capacitors in each reactive reservebasin voltage control area are given. The order of voltage control areasin the report of voltage control area reactive supply reserves for aparticular reactive reserve basin is based on the sequence of reserveexhaustion during computation of the Q-V curve. The order of voltagecontrol areas aid in indicating the order of exhaustion as voltagecollapse is approached for any contingency for that reactive reservebasin. The order of the contingencies presented in the output report fora reactive reserve basin is based on the percentage of pre-contingencyreactive reserves exhausted with the contingency causing the largestpercentage reduction reported first. The order of the reactive reservebasins presented in the output report is sorted so that the reactivereserve basins that experience the largest percentage exhaustion ofreactive supply on generators and switchable shunt capacitors for thatreactive reserve basin's worst contingency are reported first.

The contingency selection routine assists the user in determining thereactive reserve basins that experience voltage instability because theywould be the first to be reported. If no reactive reserve basinexperience voltage instability, the reporting of the reactive reservebasins in the order of the largest percentage reduction in totalreserves gives only a partial indication of the reactive reserve basinwith the most severe contingencies. Percentage reduction in totalreactive reserves of a reactive reserve basin is an excellent indicatorof the worst contingency in a reactive reserve basin and the mostvulnerable reactive reserve basin when the system is experiencing or isnearly experiencing voltage instability. The number of voltage controlareas in a reactive reserve basin that exhausts reserves and the statusof whether or not reactive reserves are exhausted on voltage controlareas listed at the end of the list given for that reactive reservebasin are effective indicators in judging proximity to voltageinstability when the contingency does not bring a reactive reserve basinclose to voltage instability. The reason for utilizing both indicatorsfor voltage collapse proximity rather than percentage reactive reservereduction is that the system experiences a quantum step toward voltageinstability after each successive voltage control area experiencesreserve exhaustion, and experience indicates voltage control areas thatexhaust reserves near the Q-V curve minimum for the pre-contingency caseare near the Q-V curve minimum for most contingencies.

An alternative embodiment of the contingency selection routine wouldfurther include modifying the set of reactive reserve basin voltagecontrol areas reserve level for contingencies that lie in the pathbetween a reactive reserve basin voltage control area and the testvoltage control area. Such contingencies can have a reactive reservebasin that does not contain the pre-contingency reserve basin voltagecontrol area that is totally or partially disconnected from the testvoltage control area by the line outage contingency. Contingencies thathave a modified reactive reserve basin and the voltage control area thatshould be deleted from the pre-contingency reactive reserve basin bothcan be detected by looking for contingencies where a reactive reservebasin voltage control area experiences little reduction in reservecompared to other severe contingencies. The deletion of these voltagecontrol areas from reactive reserve basins for those contingencies willmake the contingency ranking based on reactive reserve basin reactivereserves more accurate without requiring the user to make judgments.

In FIG. 8, performing a reactive reserve basin security assessment isillustrated by a flow chart. An initialization step is performed inblock 230 wherein selected data is retrieved. This data includes basecase simulation data, values of alpha, values of a lower voltage limitwhere attempts to compute a Q-V curve minimum are aborted, and thecriterion used for selecting the reactive reserve basin voltage controlareas.

In block 232, each critical voltage control area is specified along withits test bus. The lists of single line outage, double line outage,single loss of generation, double loss of generation, and combinationcontingencies are read in block 234.

In block 236, the Q-V curves are computed for each contingency specifiedfor the base case for each voltage control area. In conditional block238, a check for a positive Q-V curve minimum is performed. If a Q-Vcurve has a positive minimum, then execution of the routine is stopped.If there are no positive Q-V curve minima, then execution of the routineproceeds to block 240.

In block 240, a transfer pattern and level are read and a Q-V curve iscomputed for each contingency and voltage control area. Conditionalblock 242 checks whether or not there is a Q-V curve with a positiveminimum. If a Q-V curve with a positive minimum exists, then executionof the routine is stopped. Otherwise, the transfer level is increaseduntil a positive Q-V curve minimum is obtained in block 244. If, atblock 246, there are additional transfer patterns which need evaluation,then flow of the routine is directed back up to block 240. If noadditional transfer patterns need evaluation, then a load pattern andlevel is read in block 248, and a Q-V curve is computed for eachcontingency and voltage control area. If there is a Q-V curve with apositive minimum as detected by conditional block 250, then execution ofthe routine is stopped. Otherwise, the load level is increased until apositive Q-V curve minimum is obtained in block 252. If, at block 254,additional transfer patterns need evaluation, then flow of the routineis directed back up to block 248. If no additional transfer patternsneed evaluation, then execution of the routine is completed.

Ideally, the computed reactive reserve basins are robust. Robustnessimplies that the voltage control areas that experience near exhaustionof reserves for all reactive supply and voltage control devices at theQ-V curve collapse point in the pre-contingency case can experienceexhaustion of reserves at the Q-V curve collapse point after: any singlecontingency, transfer, or loading pattern change; or after anycombination line outage and loss of reactive resource contingency; orafter any combination line outage/loss of reactive resource contingencyand any transfer or loading change in any pattern. Demonstrating thatthe reactive reserve basins are robust based on the above definition isillustrated by the flow chart in FIG. 9.

In block 260, a set of line outage contingencies, loss of resourcecontingencies, transfers, real power loading pattern changes, operatingchanges, and combination line outage/loss of resource contingencies thatare known to exhaust reactive reserves in one or more specified reactivereserve basins as well as test buses in critical voltage control areasfor computing the Q-V curves that produce each of these reactive reservebasins are provided as input to the routine. These inputs can beprovided from the output of the contingency selection routine.

In block 262, the voltage control areas belonging to a specifiedreactive reserve basin are determined by computing the Q-V curve and itsminimum for each single or double contingency or operating changespecified. The reactive reserve basins of the Q-V curve computed at atest bus in a critical voltage control area for each single or doublecontingency or operating change are outputted into a table for thatcritical voltage control area by block 264. This table is used toconfirm that contingencies or operating changes do not exhaust reserveson voltage control areas where all reactive supply and voltage controlreserves are not nearly or completely exhausted when a Q-V curve iscomputed for the pre-contingency case at a test bus in a criticalvoltage control area.

Performing an intelligent voltage stability security assessment isillustrated by the flow chart in FIG. 10. The procedure involvesdetermining, at block 270, the voltage control areas, i.e. the busclusters where the Q-V curves computed at any bus have the same shapeand the same curve minimum, and the same reactive reserve basin. Thesebus clusters are found based on coherency, in other words, the samevoltage and angle changes are exhibited at all buses in the voltagecontrol area due to any disturbance. Alternatively, the bus clusters arefound based on controllability, observability, or modal properties.

Next, the subset of all of the reactive supply resources within voltagecontrol areas that exhaust all of their reactive supply at the minimumof the Q-V curve computed at any bus in the test voltage control area isdetermined at block 272. The minimum of the Q-V curve can generally beobtained using a normal Newton-Raphson algorithm using a standardprocedure that will obtain the minimum when the direct application ofthe Newton-Raphson algorithm would stop obtaining solutions short of theminimum.

A second condition for buses to belong to a voltage control area is thatthe Q-V curve computed at each bus in a test voltage control areaexhausts the same reactive supply resources in the same set of voltagecontrol areas at the Q-V curve minimum. The subset of reactive supplyresources in a system exhausted at the Q-V curve minimum is called thereactive reserve basin for that voltage control area. The slope of theQ-V curve decreases discontinuously each time all of the reactive supplyreserves in one of the voltage control areas in the reactive reservebasin is exhausted. The reactive supply from a reactive reserve basinvoltage control area to the test voltage control area is maintained aslong as one of the voltage controls associated with reactive supplydevices in a voltage control area is active and holds the voltage inthat voltage control area.

The discontinuity in the slope of the Q-V curve occurs not only due toloss of reactive supply from the reactive reserve basin voltage controlarea, but occurs due to the increased rate of increase in reactivelosses with voltage decline that accompanies loss of all voltage controlin a voltage control area. The reactive reserve basins are computed foronly selected subsets of voltage control areas that are predicted to bevulnerable to voltage instability. The voltage control areas that canexperience voltage collapse are predicted by determining those that havelarge shunt capacitive supply or experience large reactive network losschange for Q-V curves computed to determine the reactive reserve basinfor a neighboring voltage control area.

A further step entails determining, at block 274, those reactive reservebasins and their associated test voltage control areas that are mostvulnerable to single or multiple contingencies. The five worstcontingencies, which either cause voltage collapse by exhausting allreactive reserves in the reactive reserve basin or bring the reactivereserve basin closest to voltage instability by exhausting the largestpercentages of the reactive reserves in that reactive reserve basin, arealso found at block 276.

A file of single worst line outage contingencies that exhaust P% or moreof the reactive reserves in any reactive reserve basin is produced atblock 280. Further, a list of worst generator outage contingencies whichis also produced, at block 280, by identifying the two largest capacitygenerators from each reactive reserve basin where one or more lineoutage contingencies exhaust P% or more of the reactive reserve basinreserves. These two contingency lists are used to produce, at block 282,a list of all single line outages, all single generator outages, alldouble line outages, all double generator outages, and combination lineand generator outages. Also, a list of test voltage control areas whereP% or more of the reactive reserves were exhausted by single lineoutages is produced.

These files are used to compute Q-V curve minima and reactive reservebasin voltage control areas with reactive reserves for every contingencyin the lists for each reactive reserve basin test voltage control areaspecified. Although the number of contingencies in the lists ispreferably limited to the projected ten worst contingencies, a user maybe allowed to run all of the other contingencies.

In block 284, a security assessment for single and multiplecontingencies with different transfer and loading patterns is performed.Transfer limits are determined for each anticipated transfer pattern(specified by a group of generators with increasing generation in somepercentage of the total transfer level and a group of generators withdecreasing generation in some percentage of the total transfer level).The transfer level is increased in increments and Q-V curves arecomputed for all reactive reserve basin critical voltage control areasand all single and multiple contingencies. If all Q-V curves for allsingle and multiple contingencies in every critical voltage control areahave negative Q-V reactive minima (implying voltage stability) the totaltransfer level is incremented again and all Q-V curves are recomputed.This process is repeated until one Q-V curve has Q-V curve positiveminima (implying voltage instability). The total transfer level limitfor the transfer pattern is thus determined. A transfer pattern levellimit is computed for each anticipated transfer pattern and the reactivereserve basin where the Q-V curve is positive for one or more single ormultiple contingencies is noted.

The same process is repeated for loading patterns to find those reactivereserve basins that have positive Q-V curve minima for one or morecontingencies. The reactive reserve basins that constrain each transfer(or loading pattern) and the contingencies that cause the voltageinstability for that transfer (or loading pattern) are used as the basisof designing enhancements that prevent voltage instability in thatreactive reserve basin for those contingencies and a desired level oftransfer (possibly larger than the current transfer limit). It should benoted that the general planning design criterion for voltage instabilityonly requires that a power system survive a worst combination generatorand line outage and does not require that a system survive a double lineoutage contingency.

If the load flow will not solve for some contingency, transfer patternand level, or loading pattern and level, reactive reserves are increasedin all generators in each global reactive reserve basin, one at a time.If the addition of reactive reserves in some global reactive reservebasin allows a Q-V curve load flow solution to be computed, then thecontingency, transfer pattern and level, and loading pattern and levelwould cause a voltage instability in that global reactive reserve basin.This feature allows on to determine whether a contingency, or transferor loading pattern causes a voltage instability in some other globalreactive reserve basin than the one being studied.

If one has performed the above assessment of transfer limits for eachanticipated transfer pattern and loading limits for each anticipatedloading pattern, one can determine the transfer pattern limits that needto be increased and the desired level, as well as the loading patternlimits that need to be increased and their desired levels. For eachtransfer (or loading) pattern where the design criterion is notsatisfied out to the desired limit, one knows the local reactive reservebasin or basins and the contingencies that cause voltage instability inthat reactive reserve basin or basins.

The previously described embodiments of the present invention have manyadvantages. By determining single contingencies which exhaust more thatpre-specified percentage of reactive reserves, a computationallyefficient method of performing multiple contingency analysis results.The resulting method is capable of selecting multiple loss of reactiveresources, line outages, and combinations thereof, for performing ananalysis of the effect of multiple contingencies on each reactivereserve basin. Furthermore, embodiments of the present invention arecapable of identifying the specific critical voltage control area andreactive reserve basin that is brought to voltage instability after somecontingency by a particular transfer or loading pattern change that cancause voltage instability in a voltage control area.

Another advantage is that the present invention identifies a globalstability problem and each local voltage stability problem. The loss ofstability for each such problem is caused by a lack of sufficientreactive supply to its critical voltage control area. The reactivereserve basin in the critical voltage control areas that maintainvoltage and thereby prevent the reactive losses that consume and chokeoff reactive supply from outside, as well as inside, the respectivereactive reserve basin from reaching the critical voltage control area.A global voltage stability problem generally has many individual localvoltage stability problems and each can occur due to differentcontingencies or in some cases due to the same severe contingencies thatcause loss of local voltage stability for several critical voltagecontrol areas by exhausting their reactive reserve basin reserves. Theadvantages still further include detecting each critical voltage controlarea, its reactive reserve basin, the severe single and multiplecontingencies that cause voltage instability in several local reactivereserve basins and may even cause a global voltage instability.

While the best modes for carrying out the invention have been describedin detail, those familiar with the art to which this invention relateswill recognize various alternative designs and embodiments forpracticing the invention as defined by the following claims.

What is claimed is:
 1. A method of performing a contingency analysis fora region of an electric power transmission system having a plurality ofbuses and a plurality of sources of reactive reserves coupled thereto,the method comprising:grouping the plurality of buses into a pluralityof voltage control areas such that each of the plurality of buses withineach voltage control area has a similar corresponding reactive powerversus voltage relationship; determining a reactive reserve basin for atleast one of the plurality of voltage control areas, the reactivereserve basin comprising at least one of the sources of reactivereserves selected in dependence upon a measure of the depletion ofreactive reserves at a predetermined operating point of the electricpower transmission system; performing a single contingency analysis bycomputing a corresponding quantity for each reactive reserve basin inresponse to each of a plurality of single contingencies, wherein thecorresponding quantity is representative of a reduction in reactivereserves within the reactive reserve basin; and performing a multiplecontingency analysis, for each reactive reserve basin, based upon thesingle contingencies whose corresponding quantity exceeds apredetermined threshold.
 2. The method of claim 1 wherein grouping aplurality of buses comprises:determining whether each of the pluralityof buses within each of the plurality of voltage control area has asubstantially similar reactive margin at the minimum of thecorresponding reactive power versus voltage relationship; determiningwhether each of the plurality of buses within each of the plurality ofvoltage control area has a substantially similar voltage at the minimumof the corresponding reactive power versus voltage relationship; anddetermining whether each of the plurality of buses within each of theplurality of voltage control area has a substantially similar reactivereserve basin at the minimum of the corresponding reactive power versusvoltage relationship.
 3. The method of claim 1 wherein determining acorresponding reactive reserve basin comprises:selecting the at leastone of the voltage control areas whose buses therewithin have a voltageat the minimum of the corresponding reactive power versus voltagerelationship which exceeds a voltage threshold; and selecting the atleast one of the voltage control areas whose buses therewithin have areactive margin at the minimum of the corresponding reactive powerversus voltage relationship which is less than a reactive marginthreshold.
 4. The method of claim 3 wherein determining a correspondingreactive reserve basin further comprises selecting the at least onesource of reactive reserves from the voltage control areas whosereactive reserves therewithin are depleted beyond a predeterminedthreshold at the predetermined operating point.
 5. The method of claim 1wherein the predetermined operating point is the minimum of thecorresponding reactive power versus voltage relationship.
 6. The methodof claim 1 wherein the plurality of single contingencies comprises asingle generator outage.
 7. The method of claim 1 wherein the pluralityof single contingencies comprises a single line outage.
 8. The method ofclaim 1 wherein performing a multiple contingency analysiscomprises:varying a transfer pattern and level for the electric powertransmission system; and varying a loading pattern and level for theelectric power transmission system.
 9. A method of performing a voltagestability assessment for a region of an electric power transmissionsystem having a plurality of buses and a plurality of sources ofreactive reserves coupled thereto, the method comprising:grouping theplurality of buses into a plurality of voltage control areas such thateach of the plurality of buses within each voltage control area has asimilar corresponding reactive power versus voltage relationship;selecting at least one of the voltage control areas whose busestherewithin have a voltage at the minimum of the corresponding reactivepower versus voltage relationship which exceeds a voltage threshold;determining a reactive reserve basin for the at least one of theplurality of voltage control areas, the reactive reserve basincomprising at least one of the sources of reactive reserves selected independence upon a measure of the depletion of reactive reserves at apredetermined operating point of the electric power transmission system;performing a single contingency analysis by computing a correspondingquantity for each reactive reserve basin in response to each of aplurality of single contingencies, wherein the corresponding quantity isrepresentative of a reduction in reactive reserves within the reactivereserve basin, and wherein the plurality of single contingenciesincludes at least one single generator outage and at least one singleline outage; selecting the single contingencies whose correspondingquantity exceeds a predetermined threshold; and assessing the voltagestability for single and multiple contingencies with a plurality oftransfer and loading patterns, wherein the single and multiplecontingencies are based upon the selected single contingencies.